Milne attended high school in Invercargill in New Zealand until 1959, and then studied at the University of Otago in Dunedin (B.A.
In his dissertation, entitled "The conjectures of Birch and Swinnerton-Dyer for constant abelian varieties over function fields," he proved the conjecture of Birch and Swinnerton–Dyer for constant abelian varieties over function fields in one variable over a finite field.
[1] He also gave the first examples of nonzero abelian varieties with finite Tate–Shafarevich group.
He went on to study Shimura varieties (certain hermitian symmetric spaces, low-dimensional examples being modular curves) and motives.
[2] His students include Piotr Blass, Michael Bester, Matthew DeLong, Pierre Giguere, William Hawkins Jr, Matthias Pfau, Victor Scharaschkin, Stefan Treatman, Anthony Vazzana, and Wafa Wei.